Problem: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = 10$ $a_i = a_{i-1} + 5$ What is $a_{18}$, the eighteenth term in the sequence?
Answer: From the given formula, we can see that the first term of the sequence is $10$ and the common difference is $5$ To find the eighteenth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = 10 + 5(i - 1)$ To find $a_{18}$ , we can simply substitute $i = 18$ into the our formula. Therefore, the eighteenth term is equal to $a_{18} = 10 + 5 (18 - 1) = 95$.